Introduction Evolution of ice-sheet modelling Reducing uncertainties Conclusions

Bottlenecks in Antarctic ice-sheet modelling

Frank Pattyn

Laboratoire de Glaciologie, Université libre de Bruxelles (ULB)

The Future of Earth System Modeling: Polar Climates, November 28-30, 2018, Caltech

Introduction Evolution of ice-sheet modelling Reducing uncertainties Conclusions

Shepherd et al. (2018)

Introduction Evolution of ice-sheet modelling Reducing uncertainties Conclusions

Shepherd et al. (2018)

Fuerst et al. (2016)

Introduction Evolution of ice-sheet modelling Reducing uncertainties Conclusions

Marine ice sheet instability (MISI)

Shepherd et al. (2018)

Weertman (1974) –Thomas and Bentley(1978)Ice discharge acrossGL should increasewith hIce sheet onupsloping (retrograde)bedrock: slight retreat→ increase in h→increase in flux(positive feedback)

Introduction Evolution of ice-sheet modelling Reducing uncertainties Conclusions

Ice-sheet modelling: from diffusive to advective

Mercer (1978)

Huybrechts (1990)

MISI identified as potential destabilization inthe 1970sEarly 1990s: Ice sheet modelling emergedfrom paleo studiesIce sheets as a diffusive thermomechanicalsystem interacting with climate on long timescalesEuropean Ice Sheet ModellingIntercomparison (EISMINT): tests onthermomechanical ice sheet models(Huybrechts et al., 1996; Payne et al., 2000)

Introduction Evolution of ice-sheet modelling Reducing uncertainties Conclusions

From shallow-ice to full-Stokes: stiff equations

Conservation of mass

dρdt

+∇ · (vρ) = 0⇒ ∇ · v = 0

Conservation of linear momentum

ρdvdt

= ∇ · σ − ρg⇒ ∇ · σ = ρg

Conservation of energy

ρc[∂T∂t

+ v · ∇T]= ∇ · (k∇T )− 1

2trace(τ ε)

A constitutive equation relates stress to strain

τ = 2ηε , η =12

A−1/nε(1−n)/ne

Introduction Evolution of ice-sheet modelling Reducing uncertainties Conclusions

Approximations to the Stokes equations

Ice sheet: vertical shearingShallow-Ice Approximation (SIA)

Ice shelf: longitudinal stretchingShallow-Shelf Approximation (SSA)

Transition zones: all stresses equally important: full Stokes, HOM, Hybrid models

Introduction Evolution of ice-sheet modelling Reducing uncertainties Conclusions

Grounding lines: not only a Stokes problem

Hindmarsh (1996): Passiverole of ice shelves – neutralequilibrium for grounding lines(GL)Vieli & Payne (2005): GLresponse highly dependent onspatial resolutionPattyn et al. (2006): neutralequilibrium function of width oftransition zoneGladstone et al. (2010):further progress oninterpolations aroundgrounding lines

Introduction Evolution of ice-sheet modelling Reducing uncertainties Conclusions

Dynamical processes related to ice flow not included in current models butsuggested by recent observations could increase the vulnerability of the ice sheetsto warming, increasing future sea level rise. Understanding of these processes islimited and there is no consensus on their magnitude. (IPCC, AR4, 2007)

ice sheet models

# people claiming

need improvement# people improving models

Introduction Evolution of ice-sheet modelling Reducing uncertainties Conclusions

Mathematical proof for MISI

Schoof (2006, 2007)qualitatively confirmsWeertman (1974);Thomas and Bentley(1978)GL is free boundaryproblem: twoindependentconditions at movingboundary (one ofwhich is flotationcriterion)∂h∂t

= a− ∂(uh)∂x

= 0

⇒ q = ax

Introduction Evolution of ice-sheet modelling Reducing uncertainties Conclusions

MISMIP: unique GL positions and hysteresis

Pattyn et al. (2012)

Introduction Evolution of ice-sheet modelling Reducing uncertainties Conclusions

Model improvements lead to reduced uncertainty (PIG)

Durand and Pattyn (2015): Better understanding of GL behaviour led to reduced uncertainties in modelresponse to forcing since AR5 (Pine Island Glacier)

Introduction Evolution of ice-sheet modelling Reducing uncertainties Conclusions

Ice sheet

Ocean

Antarctic bedRetrograde slope

MISI: retrograde slope

Grounding line

MICI: pro/retrograde slopes

Pro/retrograde slope

Flux at the grounding line

Heat

Retreating grounding line

Cliff failure

Hydro-fracturing

a

b

Difference between MISI (Marine Ice Sheet Instability) and MICI (Marine Ice Cliff Instability). MICI results inhigh-end SLR but is atmosphere-driven (not ocean); Pattyn et al. (2018); Vermeersen et al. (2018)

Introduction Evolution of ice-sheet modelling Reducing uncertainties Conclusions

Numerical uncertainties

Seroussi and Morlighem (2018): Significant overestimation of the rate of GL retreat when melt is smeared outacross the GL.Reese et al (2018): Parametrization of buttressing may yield unphysical results (only diagnostic test).

Introduction Evolution of ice-sheet modelling Reducing uncertainties Conclusions

Physical parameter uncertainty

Bulthuis et al. (subm.): f.ETISh + emulators: Large sensitivity in response to basal conditions and the waysub-shelf melt relates to ocean conditions; complex PDFs

Introduction Evolution of ice-sheet modelling Reducing uncertainties Conclusions

Improvements on model initialization

Modelinitialization withobserved surfacevelocities(assimilation)Test basal slidinglaw for best fit ofobservedchanges invelocity(Gillet-Chaulet etal., 2016)PIG: plasticsliding law (m=5)

Introduction Evolution of ice-sheet modelling Reducing uncertainties Conclusions

Pattyn (2017): abuk experiment: GL retreat rates are highly dependent on basal processes.

Introduction Evolution of ice-sheet modelling Reducing uncertainties Conclusions

Tipping points of the Antarctic ice sheet

Applied forcing for restricted time periods (<500 year) — analysis of ice sheet response (ASE) on multi-millennialtime scales. Some MISIs engage after >2500 years — >30% increase in melt energy irrevocably leads to MISI(Durand, Sun, Pattyn)

Introduction Evolution of ice-sheet modelling Reducing uncertainties Conclusions

Effect of bedrock resolution

Durand et al. (2009); Waibel et al. (2018)

Data collectionand archiving(bed elevation,ice thickness,bathymetry) isessential forimprovingISMs

Griddedproducts arenot always themostappropriategiven adaptivegrids/unstruc-turedmeshing

Introduction Evolution of ice-sheet modelling Reducing uncertainties Conclusions

Conclusions

Paradigm shift in ice sheet modelling from slow diffusive system to rapid (unstable)system and improved understanding of marine ice-sheet mechanicsSpread in response still due to (i) uncertainties in boundary conditions and potentialfeedbacks; (ii) increased number of ice-sheet models; (iii) numerical uncertainties inmodels; (iv) bedrock/bathymetry uncertaintiesMISMIPs have a positive effect on model development:

Model ‘sorting’ based on how GL is represented becomes possible, reducing uncertaintiespresent in SeaRISEMISMIP tests are however not inclusive (lack of validation)Further MISMIPs are on their way (MISMIP+, MISOMIP, InitMIP, ABUMIP, ...)InitMIP: demonstrated importance of model initialization (data assimilation versuspaleo-spinup)

Short-term response remains hampered by these structural uncertainties, hamperingvalidation and hindcasting of ISMs for short time predictions/projections